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Investigating the interactions between Allee effect and harvesting behaviour of a single species model: An evolutionary dynamics approach

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  • Liu, Yanwei
  • Zhang, Tonghua
  • Liu, Xia

Abstract

In this study, we propose an ecological model, which is based on the Smith growth model and subject to multiplicative Allee effect. We then investigate the equilibrium bifurcation induced by the harvesting behaviour and the Allee effect, and pitch fork bifurcation and saddle node bifurcation may occur. Assuming that the carrying capacity and harvesting rate obey a Gaussian distribution, we then consider the evolutionary dynamics by using continuous strategy evolutionary game theory. Our study shows that strong Allee effect and low harvesting rate can induce bistability. It also suggests that evolution prevents extinction even if population has strong Allee effect. Numerical analysis shows that the evolutionary model can admit up to nine equilibrium points including up to four Evolutionary Stable Strategy equilibria.

Suggested Citation

  • Liu, Yanwei & Zhang, Tonghua & Liu, Xia, 2020. "Investigating the interactions between Allee effect and harvesting behaviour of a single species model: An evolutionary dynamics approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 549(C).
    • Handle: RePEc:eee:phsmap:v:549:y:2020:i:c:s0378437120301060
    DOI: 10.1016/j.physa.2020.124323
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    References listed on IDEAS

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    1. Liu, Xia & Zhang, Tonghua & Meng, Xinzhu & Zhang, Tongqian, 2018. "Turing–Hopf bifurcations in a predator–prey model with herd behavior, quadratic mortality and prey-taxis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 496(C), pages 446-460.
    2. Sun, Kaibiao & Zhang, Tonghua & Tian, Yuan, 2017. "Dynamics analysis and control optimization of a pest management predator–prey model with an integrated control strategy," Applied Mathematics and Computation, Elsevier, vol. 292(C), pages 253-271.
    3. Liu, Lidan & Meng, Xinzhu & Zhang, Tonghua, 2017. "Optimal control strategy for an impulsive stochastic competition system with time delays and jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 477(C), pages 99-113.
    4. Peng, Yahong & Zhang, Tonghua, 2016. "Turing instability and pattern induced by cross-diffusion in a predator-prey system with Allee effect," Applied Mathematics and Computation, Elsevier, vol. 275(C), pages 1-12.
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